Carr, who is chairman of British Gas owner Centrica and was chair of Cadbury during its controversial takeover by US multinational Kraft, is expected to be announced as BAE's incoming chairman as early as this week.
The 66-year-old will replace Dick Olver, who was criticised for his role in the failed, and politically fraught, attempt to merge BAE with EADS, the Franco-German owner of Airbus.
Olver, who has held the £725,000-a-year chairmanship for nine years, quit after investors called on him to quit in the wake of the aborted deal, which failed in the face of opposition from the German chancellor, Angela Merkel.
Neil Woodford, head of UK equities at Invesco Perpetual, the fund that holds £30bn of investments in firms including BAE, had demanded Olver stand down a year earlier than planned because of his dogged pursuit of a deal that would have created the world's biggest defence and civil aerospace firm with 223,000 staff across more than 50 countries.
It is understood that Woodford has been impressed with Carr's performance at Centrica and supports his appointment at BAE. Invesco Perpetual holds a 13% stake in BAE and a 5% stake in Centrica.
ShareSoc, the largest UK lobby group for individual investors, had written to its members recommending they vote against Olver's re-election at the annual meeting in May. It suggested members ask: "Why does Mr Olver feel it necessary to hang around awaiting his replacement rather than departing immediately?"
Carr's appointment to lead Britain's biggest defence company has had to be approved by the Ministry of Defence, which holds a "golden share" that requires a majority of BAE's board members being British. His appointment will trigger his retirement from the chair of Centrica later this year. He will also stand down as president of the CBI, where he will be replaced by the BT chairman, Sir Mike Rake.
BAE which employs 88,200 people, including 32,800 in the UK, sold £17.8bn worth of fighter jets, submarines, drones and other defence equipment last year. It is Britain's largest manufacturing employer and David Cameron supported the EADS deal in the hope that it would have preserved Airbus's manufacturing footprint in the UK, where the aerospace firm builds the wings for jets including the A380 superjumbo.
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